But that society is not in any way analagous to a Muslim society that is, let's face it, more devout as a society that our society is (as Christian). Iraq? Sure, there may be many conversions, because a large segment of the population is or has been secular. But there aren't many, if any, Sunnis or Shias converting.
You are wrong.
There are untold numbers of those branches of Islam converting in family blocks and even community blocks. MIRACULOUSLY because of spontaneous dreams and visions of JESUS by key family members or several family/community members.
They learn from the vision or dream that Jesus is God. But then they have to find a Bible somehow to learn just who Jesus is because they lack enough education to have a clue.
This sort of phenomena has been increasingly happening all across the Moslem world for years and is very under reported.
Again, you need to do more homework before allowing your biases to set up rock hard.